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Combinatorics of geometrically distributed random variables: Lefttoright maxima
 Discrete Mathematics
, 1996
"... Abstract. For words of length n, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, q–analogues for these parameters from the usual permutation model are obtained. 1. ..."
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Cited by 39 (9 self)
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Abstract. For words of length n, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, q–analogues for these parameters from the usual permutation model are obtained. 1.
The Average Case Analysis of Algorithms: Mellin Transform Asymptotics
, 1996
"... This report is part of a series whose aim is to present in a synthetic way the major methods of "analytic combinatorics" needed in the averagecase analysis of algorithms. It reviews the use of MellinPerron formulae and of Mellin transforms in this context. Applications include: divideandconquer ..."
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Cited by 12 (0 self)
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This report is part of a series whose aim is to present in a synthetic way the major methods of "analytic combinatorics" needed in the averagecase analysis of algorithms. It reviews the use of MellinPerron formulae and of Mellin transforms in this context. Applications include: divideandconquer recurrences, maxima finding, mergesort, digital trees and plane trees.
Analysis of an Optimized Search Algorithm for Skip Lists
 Theoretical Computer Science
, 1994
"... It was suggested in [8] to avoid redundant queries in the skip list search algorithm by marking those elements whose key has already been checked by the search algorithm. We present here a precise analysis of the total search cost (expectation and variance), where the cost of the search is measured ..."
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Cited by 11 (3 self)
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It was suggested in [8] to avoid redundant queries in the skip list search algorithm by marking those elements whose key has already been checked by the search algorithm. We present here a precise analysis of the total search cost (expectation and variance), where the cost of the search is measured in terms of the number of keyto key comparison.These results are then compared with the corresponding values of the standard search algorithm. 1 Introduction Skip lists have recently been introduced as a type of listbased data structure that may substitute search trees [9]. A set of n elements is stored in a collection of sorted linear linked lists in the following manner: all elements are stored in increasing order in a linked list called level 1 and, recursively, each element which appears in the linked list level i is included with independent probability q (0 ! q ! 1) in the linked list level i + 1. The level of an element x is the number of linked lists it belongs to. For each elemen...
Combinatorics of Geometrically Distributed Random Variables: Value and Position of the rth LefttoRight Maximum
 Discrete Math
"... For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth lefttoright maximum, for fixed r and n !1. 1. ..."
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Cited by 8 (5 self)
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For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth lefttoright maximum, for fixed r and n !1. 1.
The Number of Distinct Values in a Geometrically Distributed Sample
"... For words of length n, generated by independent geometric random variables, we consider the average and variance of the number of distinct values (= letters) that occur in the word. We then generalise this to the number of values which occur at least b times in the word. 1. ..."
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Cited by 8 (2 self)
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For words of length n, generated by independent geometric random variables, we consider the average and variance of the number of distinct values (= letters) that occur in the word. We then generalise this to the number of values which occur at least b times in the word. 1.
On the Cost of Persistence and Authentication in Skip Lists
"... We present an extensive experimental study of authenticated data structures for dictionaries and maps implemented with skip lists. We consider realizations of these data structures that allow us to study the performance overhead of authentication and persistence. We explore various design decisions ..."
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Cited by 6 (4 self)
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We present an extensive experimental study of authenticated data structures for dictionaries and maps implemented with skip lists. We consider realizations of these data structures that allow us to study the performance overhead of authentication and persistence. We explore various design decisions and analyze the impact of garbage collection and virtual memory paging, as well. Our empirical study confirms the efficiency of authenticated skip lists and offers guidelines for incorporating them in various applications.
Optimal And Nearly Optimal Static Weighted Skip Lists
"... . We consider the problem of building a static (i.e. no updates are performed) skip list of n elements, given these n elements and the corresponding access probabilities or weights. We develop a dynamic programming algorithm that builds an optimal skip list in the sense that the average access cost ..."
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Cited by 5 (0 self)
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. We consider the problem of building a static (i.e. no updates are performed) skip list of n elements, given these n elements and the corresponding access probabilities or weights. We develop a dynamic programming algorithm that builds an optimal skip list in the sense that the average access cost is minimized. We also consider nearly optimal skip lists, whose average access cost is not optimal but good enough, and can be built more efficiently than optimal skip lists. Several related issues are also discussed, for instance, other approaches to the construction of nearly optimal skip lists or the construction of optimal skip lists that minimize different kinds of search costs. 1. Introduction There are many instances where we have to deal with a static data set, i.e. no insertions, deletions or modifications are needed, and therefore it is convenient to organize the information to make the accesses to that information as efficient as possible. Just to mention a few such instances, co...
Combinatorics of Geometrically Distributed Random Variables: Run Statistics
 In preparation
, 2000
"... For words of length n, generated by independent geometric random variables, we consider the mean and variance, and thereafter the distribution of the number of runs of equal letters in the words. In addition, we consider the mean length of a run as well as the length of the longest run over all word ..."
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Cited by 3 (1 self)
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For words of length n, generated by independent geometric random variables, we consider the mean and variance, and thereafter the distribution of the number of runs of equal letters in the words. In addition, we consider the mean length of a run as well as the length of the longest run over all words of length n. 1.
Skip trees, an alternative data structure to Skip lists in a concurrent approach
, 1997
"... We present a new type of search trees, called Skip trees, which are a generalization of Skip lists. To be precise, there is a onetoone mapping between the two data types which commutes with the sequential update algorithms. A Skip list is a data structure used to manage data bases which stores val ..."
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We present a new type of search trees, called Skip trees, which are a generalization of Skip lists. To be precise, there is a onetoone mapping between the two data types which commutes with the sequential update algorithms. A Skip list is a data structure used to manage data bases which stores values in a sorted way and in which it is insured that the form of the Skip list is independent of the order of updates by using randomization techniques. Skip trees inherit all the properties of Skip lists, including the time bounds of sequential algorithms. The algorithmic improvement of the Skip tree type is that a concurrent algorithm on the fly approach can be designed. Among other advantages, this algorithm is more compressive than the one designed by Pugh for Skip lists and accepts a higher degree of concurrence because it is based on a set of local updates. From a practical point of view, although the Skip list should be in the main memory, Skip trees can be registered into a secondary...
Skip List Data Structures for Multidimensional Data
, 1994
"... This report presents four new data structures for multidimensional data. All of these data structures are based on the deterministic skip list. Explanations are provided for the 2d search skip list and three different versions of the kd skip list. These structures support fast insertion and deleti ..."
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This report presents four new data structures for multidimensional data. All of these data structures are based on the deterministic skip list. Explanations are provided for the 2d search skip list and three different versions of the kd skip list. These structures support fast insertion and deletion. The third version of the kd skip list and the 2d search skip list require only O(n) space. The 2d search skip list allows semiinfinite range searches of type ([L 1 :H 1 ],[L 2 :]), or of type ([L 1 :H 1 ],[:H 2 ]) in time O(t + log n). The third version of the kd skip list seems wellsuited for range search using parallel processing. Algorithms for building, insertion, deletion and range search for all four data structures are given, along with proofs of worst case complexity for these operations. Complete C code for range search, insertion and deletion in the 2d search skip list is also presented. Key words: dynamic data structures, range search, multidimensional data, skip lists...